The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q(t) (in g) after t years is given by:
Q(t)= 1/2^t/1620
Required:
a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for Q(0), Q(1620), and Q(3240).
Answer:
(a)[tex]e^{-0.000428 t}[/tex]
Step-by-step explanation:
We are given that
Half life of radium-226=1620 yr
The quantity left Q(t) after t years is given by
[tex]Q(t)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]
a. We have to convert the given function into an exponential function using base e.
[tex]Q(t)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]
=[tex]((\frac{1}{2})^t)^{\frac{1}{1620}[/tex]
=[tex]e^{ln(1/2) t/1620}[/tex]
[tex]=e^({\frac{ln(1/2)}{1620}t)[/tex]
=[tex]e^{-0.000428 t}[/tex]
(b)
[tex]Q(0)=e^{-0.000428 \times 0}[/tex]
=1
From original function
Q(0)=1
[tex]Q(1620)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]
[tex]Q(1620)=\frac{1}{2}=0.5[/tex]
From exponential function
[tex]Q(1620)=e^{-0.000428 \times 1620}[/tex]
[tex]=0.499\approx 0.5[/tex]
[tex]Q(3240)=(\frac{1}{2})^{\frac{3240}{1620})=0.25[/tex]
[tex]Q(3240)=e^{-0.000428 \times 3240}[/tex]
Q(3240)=0.249=[tex]\approx 0.25[/tex]
Hence, verified.
Find the slope of the line containing the given pair of points. If the slope is undefined, state so.
(-1,-7) and (-6,1)
Answer:
m = [tex]-\frac{8}{5}[/tex]
Step-by-step explanation:
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{1--7}{-6--1}[/tex]
m = [tex]\frac{8}{-5}[/tex]
m = [tex]-\frac{8}{5}[/tex]
Polygon ABCD is a rectangle. What is its area? Round your answer to the nearest tenth.
(2,5)
(-4,3)
(3, 2)
(-3,0)
Answer: The correct option is A.
Step-by-step explanation:
To calculate the distance between the points, we use the formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d= distance
[tex]x_2\text{ and }x_1[/tex] are the coordinates of the points on x-axis
[tex]y_2\text{ and }y_1[/tex] are the coordinates of the points on y-axis
For the given points:
A(-4,3), B(2,5), C(3,2) and D(-3,0)
Calculating the distance CD:[tex]x_2=3\\x_1=-3\\y_2=2\\y_1=0[/tex]
Putting values in above equation, we get:
[tex]CD=\sqrt{(3-(-3))^2+(2-0)^2}\\\\d=\sqrt{36+4}=6.32units[/tex]
Calculating the distance AD:[tex]x_2=-4\\x_1=-3\\y_2=3\\y_1=0[/tex]
Putting values in above equation, we get:
[tex]AD=\sqrt{(-4-(-3))^2+(-3-0)^2}\\\\d=\sqrt{1+9}=3.16units[/tex]
To calculate the area of a reactangle, we use the equation:
[tex]Area=l\times b[/tex] ....(1)
where,
l = length of the rectangle = CD = 6.32 units
b = breadth of the rectangle = AD = 3.16 units
Putting values in equation 1, we get:
[tex]Area=6.32\times 3.16\\\\Area=20.0 \text{ square units}[/tex]
Hence, the correct option is A.
Answer:
The answer is A.
Step-by-step explanation:
I got it correct.
please help me i will give brainlist to the correct answer
Answer:
<ABC = 27
< BAC = 126
Step-by-step explanation:
<C = <B since it is an isosceles triangle. We know this since AC - AB
<C = 27 so <ABC = 27
The sum of the angles of a triangle = 180
A + B+ C = 180
A + 27+27 = 180
A + 54 =180
A = 180-54
A =126
< BAC = 126
Question 6 of 40
Which recursive formula can be used to represent the sequence
2, 6, 10, 14, 18, ... ?
& - 2
O A.
&, - 87-704
ay - 2
O B.
an - 2n-1-4
C. &-0
an - 2n-1 + 4
D.
ay - 2
an - 8-1 + 4
Gays
Step-by-step explanation:
I cannot really identify and read the provided answer options.
the solution to the sequence 2, 6, 10, 14, 18, ... is
an = 4×(n-1) + 2
recursive that is
a1 = 2
an = an-1 + 4
please pick the right option in your original problem definition that fits to this solution.
The recursive formula that represents the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.
This fixed value is called the common difference, and it is the same for all terms in the sequence.
We have,
The given sequence has a common difference of 4 between its consecutive terms.
To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.
Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:
[tex]a_2 = a_1 + 4[/tex]
Similarly, we can represent the third term (a3) as:
[tex]a_3 = a_2 + 4[/tex]
Substituting the value of a2 from the above equation, we get:
[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]
We can continue this pattern to find the recursive formula for the nth term of the sequence:
[tex]a_n = a_{n-1} + 4[/tex]
where [tex]a_1[/tex]= 2
Thus,
The recursive formula for the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
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6a + 2b = 30
6a + 9b = 51
What are a and b
Answer:
a = 18
b = 3
hope it helps
have a nice day
what is the midpoint of the segment shown below? (3,5) (2,2)
Answer:
(5/2, 7/2)
Step-by-step explanation:
Use the midpoint formula to solve for the midpoint:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\\(\frac{3+2}{2},\frac{5+2}{2})\\\\(\frac{5}{2},\frac{7}{2})[/tex]
Which function has the domain x greater-than-or-equal-to negative 11?
Given:
Consider the below figure attached with this question.
To find:
The function that has the domain [tex]x\geq -11[/tex].
Solution:
We know that, a radical function is defined for only non negative radicand.
In option A, the function is defined if
[tex]x+11\geq 0[/tex]
[tex]x\geq -11[/tex]
The domain of this function is [tex]x\geq -11[/tex]. So, option A is correct.
In option B, the function is defined if
[tex]x-11\geq 0[/tex]
[tex]x\geq 11[/tex]
The domain of this function is [tex]x\geq 11[/tex]. So, option B is incorrect.
In option C and D, the function is defined if
[tex]x+5\geq 0[/tex]
[tex]x\geq -5[/tex]
The domains of these function are [tex]x\geq -5[/tex]. So, options C and D are incorrect.
Hence, option A is correct.
Answer:
A
Step-by-step explanation:
PLEASE HELP ME WILL MARK BRAINLIEST
Answer:
C
Step-by-step explanation:
The sum of the measures of the three angles of a triangle is 180 degrees.
A
50 + 40 + 90 = 180 good
B
55 + 35 + 90 = 180 good
C
45 + 40 + 90 = 175 not good
Answer: C
the graph below shows how money has been budgeted for a certain company
The company has budgeted approximately 25% of its money on which of the following
Answer:
Shelter from a tornado should be sought:
in any of the above
in a room in the center of the first floor
in a basement
under a staircase in the center of the house
Shelter from a tornado should be sought:
in any of the above
in a room in the center of the first floor
in a basement
under a staircase in the center of the house
Which term describes the ability to repay debt?
A
capacity
B.
creditworthiness
c. capability
Answer:
B. CreditworthinessStep-by-step explanation:
❣️(◍•Jess bregoli•◍)❣️#keep learning!!Answer:
B
Step-by-step explanation:
Over what interval is the function decreasing? f(x)=(3−x)^2 + 5
Answer: It decreases on the interval (-infinity, 3)
This is the same as saying -infinity < x < 3, or simply x < 3
=============================================================
Work Shown:
f(x) = (3−x)^2 + 5
f(x) = (-x+3)^2 + 5
f(x) = (-1(x-3))^2 + 5
f(x) = (-1)^2*(x-3)^2 + 5
f(x) = 1(x-3)^2 + 5
The last equation is in the form y = a(x-h)^2 + k
We have a = 1, h = 3 and k = 5
The vertex is (h,k) = (3,5)
Since 'a' is positive, this means the function decreases on the left and increases on the right (forming a parabola that opens upward). See below.
So the function is decreasing when x < 3, which represents everything to the left of the vertex.
We can expand that out to -infinity < x < 3 which converts to the interval notation (-infinity, 3)
ASAP PLEASE!!The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed. Find the probability P(T=3). write your answer as a fraction.
Given:
The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed.
To find:
The probability [tex]P(T=3)[/tex].
Solution:
In the given table T represents the number of tails.
From the given table it is clear that the value of probability is [tex]\dfrac{1}{8}[/tex] and [tex]T=3[/tex]. So,
[tex]P(T=3)=\dfrac{1}{8}[/tex]
Therefore, the probability [tex]P(T=3)[/tex] is equal to [tex]\dfrac{1}{8}[/tex].
How to Factor 4n^3-49n
Answer:
n (2n-7) (2n+7)
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
khalil has a circular cake that he plans to share equally betweeb himself and 5 friends. if tge cake is 8 inched in a diameter, what will be the length of the arc of each slice of cake.
Answer:
4.2
Step-by-step explanation:
It would be 8/2 which gets 4 and put the .2 4.2
Length of the arc of each slice of cake is equals to 5.024inches.
What is length of the arc?
" Length of the arc is defined as the distance between any two points as a part of the circumference of the circle."
Formula used
Length of the arc = radius × central angle of the arc
l = r × θ
According to the question,
Number of friends = 5
Diameter of the cake = 8inches
Shape of the cake is circular.
Therefore angle formed = 360°
Angle for each piece of cake = [tex]\frac{360}{5}[/tex]
= 72°
Radius of the cake = [tex]\frac{diameter }{2}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4 inches
Substitute the value in the formula to get the length of the arc we get,
L = 4 × 72 × [tex]\frac{\pi }{180}[/tex]
= 5.024inches
Hence, length of the arc of each slice of cake is equals to 5.024inches.
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Factor the trinomial, or state that the trinomial is prime.
y2-9y+14
Please help
=====================================================
Explanation:
To factor this, we need to find two numbers that
A) multiply to 14 (last term)B) add to -9 (middle coefficient)Through trial and error, you would find that the two numbers are -2 and -7
-2*(-7) = 14
-2 + (-7) = -9
So that's why the given trinomial factors to (y-2)(y-7)
You can use the FOIL rule to go from (y-2)(y-7) back to y^2-9y+14 again.
-1/13-10/39 in lowest terms
Step-by-step explanation:
the answer is already as simplified as it could be
2
Question 10 Multiple Choice Worth 5 points)
(06 02 MC)
Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations?
1
5x + 2y = 2
3x - 3y = 18
The slopes are the same, and the y.Intercepts are the same
The slopes are the same, and the y-intercepts are different
The slopes are different, and the y-intercepts are the same
Previous Question
Question 1 (Answered)
ON
Type here to search
O
BE
C
84'F Rain coming
AG
Answer:
the slopes are different, and the y-intercepts are also different
Step-by-step explanation:
We can rewrite the equations given in slope-intercept to easily determine the slope (m) and the y-intercept (b). Slope-intercept equation is y = mx + b
Let's rewrite each equation:
✔️5x + 2y = 2
Subtract 5x from each side
2y = -5x + 2
Divide both sides by 2
y = -5x/2 + 2/2
y = -⁵/2(x) + 1
The slope (m) = -⁵/2
y-intercept (b) = 1
✔️3x - 3y = 18
Subtract 3x from each side
-3y = -3x + 18
Divide both sides by -3
y = -3x/-3 + 18/-3
y = x - 6
Slope (m) = 1
y-intercept (b) = -6
✅Therefore, the slopes are different and the y-intercepts are also different
i need the answer fast please
Step-by-step explanation:
everything can be found in the picture
Could you help me answer 2a, b, c and d? See the image below.
Answer:
2a. 1/4
2b. 2/8
2c. yes, 1/4 = 2/8 because
2 / 8 = 2 ÷ 2 / 8 ÷ 2 = 1 / 4.
2d. the total number of parts doubled in the denominator, the number of parts represented in the numerator doubled as well.
The operations of division and multiplication are made proportionally to the numerator and denominator.
GIVING OUT BRAINLIEST PLEASE HELP ME!!
Answer: B (0,0) r=4
Step-by-step explanation:
How much would the combined production of pineapples increase for the two islands due to trade? How much would the combined production of pearls increase?
Step-by-step explanation:
find the coordinate of the foot of the perpendicular from(4,-2) to the line 2x-3y-4=0
PYTHAGORAS
work out the side of b.
give your answers to one decimal place
Answer:
12 cm
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
a = 12 cm
c = 17 cm
Step 2: Solve for b
Substitute in variables [Pythagorean Theorem]: 12² + b² = 17²Evaluate exponents: 144 + b² = 289[Subtraction Property of Equality] Subtract 144 on both sides: b² = 145[Equality Property] Square root both sides: b = √145[√Radical] Evaluate: b = 12.0416Round: b ≈ 12.0Solve each equation by graphing. Round to the nearest tenth.
X^2-6x= -8
A) 4, 2
B) −4, 2
C) −2, 4
D) −2, −4
Answer:
A
Step-by-step explanation:
That is the procedure above
petrol and engine oil has to mix in the ratio 5 : 2 for a certain motorcycle how much engine oil is needed to mix with 10 litres of petrol
Answer:
Step-by-step explanation:
Set this up as a ratio of proportions of petrol : oil
[tex]\frac{p}{o}[/tex] and if the ratio of the mix has to be 5p to 2 oil then:
[tex]\frac{p}{o}:\frac{5}{2}[/tex] We need to find how much oil, x, is needed to mix with 10 liters of petrol. Completing the proportion with that ratio gives us the problem in its entirety:
[tex]\frac{p}{o}:\frac{5}{2}=\frac{10}{x}[/tex] and cross multiply
5x = 20 so
x = 4 liters of oil are needed to mix with 10 liters of petrol.
A square has an area of 81 cm2.
Find the perimeter of the square
Area = side²
=> 81cm² = side ²
=> √81cm² = side
=> 9cm = side
Perimeter = 4 × side
=> Perimeter = 4 × 9cm
=> Perimeter = 36cm
Step-by-step explanation:
[tex]here \: is \: your \: solution : - \\ \\ Given :- \\ \\ = > area \: of \: square \: = 81cm {}^{2} \\ \\ = > we \: need \: to \: find \: perimeter \\ \\ for \: this \: we \: have \: to \: find \: its \: side. \\ \\ = > area \: of \: square \: = side { }^{2} \\ \\ = > side {}^{2} = 81cm {}^{2} \\ \\ = > \: side \: = \sqrt{} 81cm \\ \\ = > side = \sqrt{9 \times 9} \\ \\ = > side \: = 9 \: cm \\ \\ now \: we \: can \: find \: (perimeter) \\ \\ = > perimeter \: of \: square \: = 4 \times side \\ \\ = > perimeter = (4 \times 9 )cm \\ \\ = > perimeter \: of \: square = 36cm \\ \\ HOPE \: IT \: HELPS \: (. ❛ ᴗ ❛.)[/tex]
Check my work
Concerns about climate change and CO2 reduction have initiated the
commercial production of blends of biodiesel (e.g., from renewable sources)
and petrodiesel (from fossil fuel). Random samples of 48 blended fuels are
tested in a lab to ascertain the bio/total carbon ratio.
(a) If the true mean is.9200 with a standard deviation of 0.0050, within what
interval will 99 percent of the sample means fall? (Round your answers to 4
decimal places.)
The interval is from
to
(
Pls solve this question:
it is about Square and square roots
if u answer, then I will mark you as brilliant
[tex]\sqrt{2.3} multiplied \sqrt{2.3[/tex]
Answer:
2.3
Step-by-step explanation:
if you mean √2.3×√2.3 then the answer is 2.3 because √2.3×√2.3= (√2.3)² and that square cuts the square root and what remains is 2.3 which is the answer.
the sum of 3 times a number and 7 is 8 use the variable of w for the unknown number
Answer:
⅓
Step-by-step explanation:
I solved it in the picture above
Answer:
w = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The equation representing the situation is
3w + 7 = 8 ( subtract 7 from both sides )
w = 1 ( divide both sides by 3 )
w = [tex]\frac{1}{3}[/tex]
There are 13 apples in a basket. 4 of these apples are green. The rest are red. what is the ratio?
Answer:
9:4 4:13
Step-by-step explanation:
Answer:
a) 9:4 b) 13 : 9
Step-by-step explanation:
13 = total
4 = green
13-4 ( which Is 9) = red
Ratio of red apples to green apples?
9:4
RATIO of all apples to red
13: 9