Answer:
Step-by-step explanation:
The decay rate of strontium-90 is -.0244 as given.
For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.
[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to
A(t) = 400(.4809461353) so
A(t) = 192.4 g
For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:
[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:
[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:
[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:
ln(.25) = -.0244t and divide by -.0244:
61.8 years = t
For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:
[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:
[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:
[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:
ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):
[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:
[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and
H = 28.4 years
Derive the explicit rule for the pattern: 3, 0, - 3, - 6, - 9, ...
Answer:
Step-by-step explanation:
a1 = 3
d = -3
an = a1 + (n - 1)*d
an = a1 + (n - 1)*-3
Try it
Let n = 5
a5 = 3 + (5 - 1)*-3
a5 = 3 + 4*-3
a5 = 3 - 12
a5 = - 9 which is exactly what it should be.
The interesting one to try is n = 2
a2 = a1 + (2 - 1)*-3
a3 = 3 + 1(-3)
a3 = 3 - 3
a3 =0
Which is exactly what the second term is. It's interesting because you would never guess that 0 is what you get.
Solve for x
-3x = -15
A) x = -45
B) x = 5
C) x = -5
C-x=-5
Step-by-step explanation:
-3x=-15
or,-3x x =-15
or, x=-15÷3
therefore, x=-5
What is 1/8+1/4 whats the answer
In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 580 chips manufactured by an existing process were tested, and 125 of them failed. Then, 780 chips manufactured by a new process were tested, and 130 of them failed. Find a 90% confidence interval for the difference between the proportions of failures for chips manufactured by the two processes. (Round the final answers to four decimal places.) The 90% confidence interval is
Answer:
The 90% confidence interval is (0.0131, 0.0845).
Step-by-step explanation:
Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Old process:
125 out of 580, so:
[tex]p_O = \frac{125}{580} = 0.2155[/tex]
[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]
New process:
130 out of 780. So
[tex]p_N = \frac{130}{780} = 0.1667[/tex]
[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]
Distribution of the difference:
[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]
[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]
The 90% confidence interval is (0.0131, 0.0845).
PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
11
find the number of ways of forming
an executive Committee of four in a
social club consisting of 15 members,
If a particular man must be in
the comittee
There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members
Understanding Permutation and CombinationIf a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:
14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364
Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.
Learn more about combination here:
https://brainly.com/question/28065038
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Please help!! Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
C
Step-by-step explanation:
the fibrin definition tells us that the first term of the sequence a1 = 6
so, B is out.
and for every following term we always add 7 to every previous term to create the next one.
so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13
not 42, not -7
therefore, only C is correct.
and 13+7 = 20
and 20+7 = 27
it all fits
Can the three values represent the sides of a triangle?
7, 8, √113
Is this a triangle?
If so, what type?
Pythagorean Triple? (yes/no)
no the square root of 113 is rounded to 56x2
i would like some help please i am stuck
Answer: -2(d) is the answer.
Step-by-step explanation:
x1 = 3
y1 = -5
x2 = -2
y2 = 5
slope (m) = rise/run = (y2 - y1)/(x2-x1)
=(5-(-5))/(-2-3)
= 10/-5
= -2
1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.
Let x be the first number in the sequence, so the first three numbers are
{x, 0.5x, 0.5²x}
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
is arithmetic, so there is some constant c such that
0.5x - 10 = x/4 + 10 + c ==> x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c ==> x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are
{160, 80, 40}
What is the equation of a line that passes through the point (8,-2) and is parallel to the line whose equation is 3x+4y=15?
Answer:
y = -3x/4 + 4
Step-by-step explanation:
slope m = -3/4
-2=(-3/4)×8+b
or, b = 4
y = mx + b
y = -3x/4 + 4
Answered by GAUTHMATH
the average temperature at the south pole is -49.62and the average temperature at north pole is -34.68. how much higher is the average temperature at the north pole than at the south pole
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
Hector's Position:
Hector was standing halfway between first and second base, at the grass line. The
grass line is 95 feet from the pitcher's mound.
6. Calculate the coordinates for Hector's position. [Note: We can assume that 95
feet is an approximately horizontal distance from the pitcher's mound to the grass
line.] (2 points: 1 for x, 1 for y)
Hector was standing at the coordinate ( __, _).
Calculate Hector's Throw:
Answer:
(137.78, 47.72)
Step-by-step explanation:
(I just finished this assignment.)
Tre's position at the pitcher's mound as the point (42.78, 42.78).
( x , y )
Hector is about 95 feet away from the pitcher's mound horizontal, (x axis).
Since we already have the correct y-coordinate, we need to solve for the correct x-coordinate.
x = 95 + 42.78
↓ ↓ ↓
95 + 42.78 = 137.72
Now all you need to do is write out the coordinates.
Hector's coordinates are (137.72, 47.78 )
When printing an article of 2400 words, an entrepreneur decides to use two sizes of letters, using the largest one a printed page contains 1200 words. Using the smallest, the page contains 1500 words the article must occupy 17 full pages in the magazine how many pages must be printed using small letters?
Step-by-step explanation:
x= Number of small pages
y= Number of full pages
1 x + 1 y = 21 .............1
Total words
1200 x + 1500 y = 27000 .............2
Eliminate y
multiply (1)by -1500
Multiply (2) by 1
-1500 x -1500 y = -31500
1200 x + 1500 y = 27000
Add the two equations
-300 x = -4500
/ -300
x = 15
plug value of x in (1)
1 x + 1 y = 21
15 + y = 21
y = 21 -15
y = 6
y = 6
x= 15 Number of small pages
y= 6 Number of full pages
What are the solutions of this quadratic equation?
4x2 + 3 = 4x + 2
Answer:
A. x = 1/2
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringStandard Form: ax² + bx + c = 0Solving quadraticsStep-by-step explanation:
Step 1: Define
Identify
4x² + 3 = 4x + 2
Step 2: Solve for x
[Equality Property] Rewrite in standard form: 4x² - 4x + 1 = 0Factor: (2x - 1)² = 0Solve: x = 1/2Bridgette bought 1 pack of white T-shirts and 5 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 2, and the blue T-shirts come in packs of 6. How many T-shirts did Bridgette buy in all?
Work Shown:
1 pack of white = 2 shirts = A
1 pack of blue = 6 shirts
5 packs of blue = 5*6 = 30 shirts = B
A+B = 2 white shirts + 30 blue shirts = 32 shirts total
Answer:
32 T-shirts in total
Step-by-step explanation:
1 white has 2
1 blue has 6
1*2=2 white T
5*6=30 blue T
30+2=32
PLEASEEEEEE HELPPPPPPPPP
what are the zeros for this?
f(x) = 2x^2 + 6x + 2
Answer:
-3/2 ±1/2 sqrt(5) = x
Step-by-step explanation:
f(x) = 2x^2 + 6x + 2
Set the function equal to 0
0 = 2x^2 + 6x + 2
Factor out 2
0 = 2(x^2 + 3x + 1)
Divide by 2
0 = (x^2 + 3x + 1)
Subtract 1 from each side
-1 = x^2 +3x
Complete the square by dividing the x coefficient by 2 and then squaring
(3/2)^2 = 9/4
-1 +9/4 = x^2 +3x+9/4
-4/4+9/4 = (x+3/2) ^2
5/4 = (x+3/2) ^2
Taking the square root of each side
± sqrt(5/4) = sqrt( (x+3/2) ^2)
±1/2 sqrt(5) = (x+3/2)
Subtract 3/2 from each side
-3/2 ±1/2 sqrt(5) = x
The value of 4√(10) -2 is
Answer:
8√2
Step-by-step explanation:
4√(10) -2
= 4√8
=4√4×2
=4×2√2
=8√2
Jim, Katrina, Larry, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim last?
c. Find the probability that Jim will arrive first and Kim last.
a.___ (Type an integer)
b.___ (Type an integer.)
c.___ (Type a fraction. Simplify your answer)
Answer:
24
6
1/12
Step-by-step explanation:
a) This is a counting problem 4*3*2*1 = 24 different ways.
b) 1 * 2 * 1 * 1 = 2 ways
This is one you should try.
Jim Kat Larry Kim
Jim Larry Kat Kim
You can't get another way.
c)
There are 2 ways that Jim can arrive first and Kim Last shown in b
2/24 = 1/12
The lengths of the parallel sides of
a trapezium are 12cm and 26cm
If Its area is 228cm square Find the
perpendicular distance between the
Parallel sides
Answer:
12 cm
Step-by-step explanation:
12+26/2 ×x =228
19x =228
X=12cm
Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
HELP PLS
Answer:
(x-4)^2=-8(y-3)
This is a parabola.
Step-by-step explanation:
Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).
p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.
The vertex is half way point between focus (4,1) and directrix y=5.
So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.
(x-h)^2=4p(y-k)
(x-4)^2=4×-2(y-3)
(x-4)^2=-8(y-3)
What is the classification for this polynomial?
-9m^2n^3
Answer:
(a) Monomial
(b) Cubic
Step-by-step explanation:
Given
[tex]-9m^2n^3[/tex]
Required
Classify
By number of terms
The above polynomial is single term.
Single term polynomials are referred to as monomial
By degrees
To determine the degree, we consider the variable farthest from the constant.
In this case, n is farther from 9 than m.
And the power or degree of n is 3.
Polynomials with degree 3 are referred to as cubic polynomial
Convert the improper fraction to a whole or mixed number. (Enter your answer as a simplified mixed number.)
25
7
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
find the missing length indicated
Answer:
Step-by-step explanation:
192
Answer:
Step-by-step explanation:
What is the area of the trapezoid?
Answer:
A=a+b
2
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
I need help ASAP pleasee
Answer:
The answer is 4 1/2
Step-by-step explanation:
Because A to C is 2 1/4 so all you have to do add 2 1/4 + 2 1/4 which will equal 4 1/2
The product of two positive integer numbers is 70 and the sum of the same two numbers is 17. Find the
numbers.
Answer:
7 and 10
Step-by-step explanation:
7 * 10 = 70
7 + 10 = 17
Answer:
10 and 7
Step-by-step explanation:
call them a and b, respectively
so a*b=70 -> b=70/a
a+b=17 ->a+70/a=17 ->a=10 b =7
Choose the correct elements in the set for the following:
{y | y is an integer and y >/= -3}
{3, 4, 5, 6, . . .}
{−2, −1, 0, 2, . . .}
{−1, 0, 1, 2, . . }
{−3, −2, −1, 0, . . .}
****PLEASE explain your answer****
Answer:
D
Step-by-step explanation:
Y => - 3 that is {−3, −2, −1, 0, . . .}
