2 The half-life of a substance is defined as the period of time it takes for the amount of the
substance to decay by half. The sequence shows the amount of a substance that will remain
after a certain number of half-lives have elapsed.
1, 1/2, 1/4, 1/8
Describe this sequence.
Answers
The given sequence is
1, 1/2, 1/4, 1/8......
we can see that the ratio of the consecutive terms is the same. We have
1/2/1 = (1/4)/(1/2) = (1/8)/(1/4) = 1/2
This means that it is a geometric sequence
To find the amount of the substance left after 21 half lifes, we would find the 21st term of the sequence. The formula for finding the nth term of a geometric sequence is
an = a1r^(n - 1)
a1 = 1
n = 21
r = 0.5
Thus,
a21 = 1 * 0.5^(21 - 1) = 0.5^20
a21 = 0.00000095367
a21 = 1/1048576
The answer makes sense in the problem context because it follows the common ratio that was established at the begining.
Related Questions
can u please help me before I get on error message, and It kicks me out the tutoring
Answers
To find the image we have to multiply every coordinate by the scale factor.
Then:
[tex]\begin{gathered} A^{\prime}(0,2) \\ B^{\prime}(9,0) \\ C^{\prime}(4,4) \end{gathered}[/tex]if Robbie can do 35 Jumping Jacks in 60 seconds how many seconds would it take him to do 14 jumping jacks
Answers
Based on the number of jumping jacks that Robbie can do in 60 seconds, the number of seconds it will take to do 14 jumping jacks is 24 seconds
How to find the number of seconds?To find the number of seconds that it takes Robbie to do 14 jumping jacks, find the number of seconds it takes to do a single jumping jack.
The number of seconds to do a single jumping jack is:
= 60 / 35
= 1.71 seconds
If 14 jumping jacks are to be done then the number of seconds would be:
= 1.71 x 14
= 24 seconds
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Your account number is 421746. You wish to deposit 120 dimes, 25 quarters, and checks for $184.63 and $196.17. You wish to receive $50.00 in cash. Complete the savings deposit slip.
Answers
The deposit slip would look like this:
we have that the currency is 120 dimes = $1.2 and 25 quarters = $6.25.
Ten bags of beans cost GH¢350.00.
a)Find the cost of 6 bags.
b)Find the cost of 11 bags.
c)How many bags can GH¢245.00
buy?
With solutions
Answers
The cost of 6 bags is GH¢ 210
The cost of 11 bags is GH¢ 385
GH¢245.00 can buy 7 bags
Tens bags cost GH¢350.00
one bags cost = 350/10
= 35
The cost of 6 bags can be calculated as follows
1 bag= 35
6= x
cross multiply both sides
x= 35×6
x= 210
The cost of 11 bags can be calculated as follows
1= 35
11= y
cross multiply
y= 35 × 11
= 385
The number of bags GH¢245.00 will buy can be calculated as follows
1 = 35
x= 245
cross multiply both sides.
35x= 245
x= 245/35
x= 7
Hence GH¢245.00 can buy 7 bags, 6 bags cost GH¢210 and 11 bags cost GH¢ 385
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Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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The second part of the problem is where i need help. The answers i have there have been given by other tutors
Answers
SOLUTION
From the given value
Since
[tex]\sin u=\frac{7}{25}[/tex]Then using trigonometrical ratios it follows
[tex]\cos u=\frac{24}{25}[/tex]Using hal -ngle it folows
[tex]\begin{gathered} sin(\frac{u}{2})=\sqrt{\frac{1-\frac{24}{25}}{2}} \\ s\imaginaryI n(\frac{u}{2})=\sqrt{\frac{1}{50}} \end{gathered}[/tex]Also
[tex]\begin{gathered} cos(\frac{u}{2})=\pm\sqrt{\frac{1+\frac{24}{25}}{2}} \\ cos(\frac{u}{2})=\sqrt{\frac{49}{50}} \\ cos(\frac{u}{2})=7\sqrt{\frac{1}{50}} \end{gathered}[/tex]Finally?
[tex]\begin{gathered} \tan(\frac{u}{2})=\pm\sqrt{\frac{1-\frac{24}{25}}{1+\frac{24}{25}}} \\ \tan(\frac{u}{2})=\sqrt{\frac{1}{49}} \\ \tan(\frac{u}{2})=\frac{1}{7} \end{gathered}[/tex]The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.Find the length of the third side c.
Answers
Statement Problem: The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.
Find the length of the third side c.
Solution:
Thus, the perimeter of a triangle with lengths a, b and c is;
[tex]P=a+b+c[/tex][tex]\begin{gathered} \text{Let a=7inches, b=5inches, P=19inches} \\ c=P-a-b \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} c=19-7-5 \\ c=7 \end{gathered}[/tex]Thus, the length of the third side is 7inches
Write the statement as a conditional statement, then tell which part is the hypothesis and which is the conclusion. Write the inverse, converse, and contrapositive of your conditional statement:
People who reduce their time in the shower will save money on water.
Answers
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
What is the conditional statement?A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
Inverse Statement: If people did not reduce their time in the shower, then they will not save money on water.
Converse Statement: If they will save money on water then people reduce their time in the shower.
Contrapositive Statement: If they will not save money on water then people do not reduce their time in the shower.
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Rewrite each explicit formula in the form of a function an = 19 - 7(n - 1)
Answers
An object moves according to a law of motion, where, its position is described by the following function, s = f(t) = t^4 - 4t + 1. The time t is measured in seconds and s in meter.a. Sketch the velocity graph and determine when is the object moving in the positivedirection.b. Draw a diagram of the motion of the object and determine the total distancetraveled during the first 6 seconds.
Answers
SOLUTION
(a) The function given is the distance graph. The velocity fuction is the derivative of the distance function. This becomes
[tex]\begin{gathered} f(t)=t^4-4t+1 \\ f^{\prime}(t)=4t^3-4 \\ v=4t^3-4 \end{gathered}[/tex]the graph is shown below
From the velocity graph above, the function is moving in a positive direction from 1 second and beyond
(b) The diagram of motion of the object is shown in the distance graph below
The total distance travelled is the integral of the velocity function from 0 to 6 as shown below
[tex]\begin{gathered} \int_0^64x^3-4 \\ =[\frac{4x^4}{4}-4x]_0^6 \\ =[x^4-4x]_0^6=6^4-4(6)-(0^4-4(0)) \\ =1296-24-0 \\ =1272 \end{gathered}[/tex]Hence the answer is 1272 m
Which of the expressions below has a sum of 0? select all that apply A. 4+(-4) B. 6.3 +(-3.6) C. 13+(-11) D. -9+9
Answers
Answer:
A. 4+(-4),
D. -9+9
Step-by-step explanation:
A expression has a sum of 0 when we have two equal numbers with inverse signals.
A. 4+(-4)
We have the same number(4), and they have inverse signals. So this expression has a sum of 0.
B. 6.3 +(-3.6)
6.3 and 3.6 are different numbers, so this expression does not have a sum of 0.
C. 13+(-11)
13 and 11 are different numbers, so this expression does not have a sum of 0.
D. -9+9
We have the same number(9), with inverse signals. So yes, this expression has a sum of 0.
A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
Answers
The probability of a candy when randomly taken is purple or not red is 0.235
Given,
Number of red candies in the bag = 42
Number of green candies in the bag = 42
Number of yellow candies in the bag = 20
Number of purple candies in the bag = 32
We have to find the probability of a candy when randomly taken is purple or not red.
Probability, P(E) = Number of favorable outcomes / Total number of favorable outcomes
Here,
Number of favorable outcomes = 32
Total number of favorable outcomes = 42 + 42 + 20 + 32 = 136
So,
P(E) = 32/136 = 0.235
That is,
The probability of a candy when randomly taken is purple or not red is 0.235
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=O EXPONENTS AND POLYNOMIALSProduct rule with positive exponents: UnivariateMultiply.-W3(-2²)Simplify your answer as much as possible.X 5?
Answers
Answer
Explanation: To solve this question we will just need to consider some rules as represented below
[tex]\begin{gathered} -a(-b)=+ab \\ x^a*x^b=x^{a+b} \end{gathered}[/tex]Step 1: Once we understand both rules above we can use them to simplify our equation as follows
[tex]\begin{gathered} -w^3(-2w^3) \\ +2*w^3*w^3 \\ 2*w^{3+3} \\ 2w^6 \end{gathered}[/tex]Final answer: So the final answer is
[tex]2w^{6}[/tex].
you make $512.92 a week. if you work 36 hours find your hourly rate of pay
Answers
The hourly rate of pay is $14.25
To solve this, w
(PLS HELP, FINAL QUESTION!!!)
which of the following lists the correct values of a, h, and k for the function: f(x)=n^2+6
A) a = 1, h = 1, k = 6
B) a = 1, h = –1, k = 6
C) a = 1, h = 0, k = 6
D) None of the choices are correct.
Answers
Answer:
N^2+6 is in standard form, which is in ax^2+bx+c,
in order to get it to vertex form, which y=a(x-h)^2+k, we need to find the vertex, through x=-b/2a, in this case:
x=-0/2(1)=0, so h=0, then plug 0 in for n,
0^2+6=6,
which makes k=6,
therefore, the answer is c.
as for a, the value of a is constant in all forms, whether standard, vertex or factored, making a=1
Brainliest pls
determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267
Answers
The relation between the function is X cannot repeat itself.
We have given that,
functions table
We have to determine which relation is a function.
What is the function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
The relation between the function is
X cannot repeat itself
Therefore option C is correct.
Complete question: Determine which of the following relations is a function [see in attachment]
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If measure of angle 3 = (5x + 12)° and measure of angle 7 = (8x)° find the value of ‘x’.
Answers
The value of x is 21
The other angles are 63°, 117°, 63°, 117°
Given:
The angles of a parallelogram ABCD are
∠A = 3x°
∠B = (5x+12)°
To find:
The value of x
Parallelogram ABCD,
∠A and ∠B are two adjacent sides
Properties of a parallelograms
Two opposite sides are parallelogram are equal and parallel to each other.
So, the adjacent sides are supplementary angles i.e. sum is 180°.
The opposite angles are equal.
Now,
∠A + ∠B = 180°
⇒ 3x + (5x + 12) = 180
⇒ 3x + 5x + 12 = 180
⇒ 8x + 12 = 180
⇒ 8x = 180 - 12
⇒ 8x = 168
⇒ x = 168 ÷ 8
⇒ x = 21
Thus,
The value of x = 21
The angles are
∠A = 3x = 3 * 21 = 63°
∠B = (5x + 12) = (5 * 21 + 12) = 105 + 12 = 117°
As opposite angles are equal so
∠A = ∠C = 63°
∠B = ∠D = 117°
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ANSWERRRRRRRRRRRRRRRRRRRRRRR
Answers
The perimeter of the figure is 22.4 cm, and The area of the figure is 30.2cm²
What is meant by Pythagoras connection?The Pythagorean theorem, or Pythagorean theorem, explains the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to Pythagoras' theorem.
From the diagram, the formation is a rectangle.
Use the coordinate points to find the measurements of each side.
Side length AD = Side length BC
Apply the Pythagoras connection to find length BC as;
a² + b²= c² where a=2 cm and b = 4 cm and c =BC
2² + 4² = c²
4+16 = c²
20 = c²
c= √20 = 4.4721
Length BC = Length AD = 4.5 cm
Side length AB = Side length DC
Apply the Pythagoras connection to find the length DC as;
a² + b²= c² where a=6 cm and b = 3 cm and c =DC
6² + 3² =c²
36 + 9 = c²
45 = c²
√45 = c
c= 6.7082
c = DC = 6.7 cm
Now you have the dimensions of the rectangle as;
Length = 6.7 cm and width = 4.5 cm
The perimeter will be ;
P= 2{l +w} --------- where l is length and w is width and P is the perimeter of the rectangle
P=2{6.7 + 4.5}
P=2{11.2}
P= 22.4 cm
The area will be ;
A= l*w
A= 6.7 * 4.5 = 30.15 = 30.2 cm²
The perimeter of the figure is: 22.4 cm
The area of the figure is: 30.2 cm²
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True or false?
A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output.
Answers
The following statement: A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output is false.
A natural monopoly is a sort of monopoly that emerges because of the high start-up costs or substantial economies of scale associated with conducting business in a certain industry, which can result in large barriers to entry for potential rivals.
Natural monopolies can form in sectors that require specialized raw resources, technology, or other variables to function. Natural monopolies can also occur when one business is far more efficient than several enterprises in providing the market with the item or service.
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Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Answers
Step 1
Given; Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 2
Let x represent miles
y represents hours
Thus the inequality will be;
[tex]speed=\frac{distance}{time}[/tex][tex]\begin{gathered} Speed\text{ is over }9mph \\ This\text{ means David drives more than 9 miles per hour} \\ speed>9mph \end{gathered}[/tex]Answer; The required inequality is > or greater than because he drives over 9mph which means > 9mph
[tex]The\text{ required inequality is }>[/tex]Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 61 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.3 and a standard deviation of 2.4. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Answers
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
What is a confidence interval?
In statistics, a confidence interval describes the likelihood that a sample size would fall between such a set range of values for a specific percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% likelihood that the true value comes inside that range if the following are examples of 10.00 produced using a statistical model with a 95% standard error of 9.50 - 10.50.In the study of chocolate chips,
sample size, n=61
mean, x=8.3
standard deviation, s=2.4
90% of the confidence interval
[tex]8.3-(\frac{1.28*2.4}{\sqrt{61} } ) < m < 8.3+(\frac{1.28*2.4}{\sqrt{61} } )[/tex]
7.9067<m<8.6933
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
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determine if f, g, and h are true or false. If false, correct the statement with an explanation
Answers
We need to determine if the statements are true or false.
In order to do so, we need to pay attention to the following notations:
[tex]\begin{gathered} (\sin x)^{-1}=\frac{1}{\sin x} \\ \\ \sin^{-1}x=\text{ inverse function of }\sin x \end{gathered}[/tex]The same notations apply to cosine and tangent functions.
The inverse f⁻¹(x) is the function such that:
[tex](f^{-1}\circ f)(x)=f^{-1}(f(x))=x[/tex]Thus, we have:
[tex]\cos^{-1}(\cos(\frac{15\pi}{6}))=\frac{15\pi}{6}[/tex]Therefore, statement g. is true.
In order to show that statements f. and h. are false, let's see what happens for x = 1/2:
[tex]\begin{gathered} \frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}=\frac{\frac{\pi}{6}}{\frac{\pi}{3}}=\frac{3}{6}=0.5\text{ \lparen no units\rparen} \\ \\ \tan^{-1}(\frac{1}{2})\cong0.46\text{ \lparen rad\rparen} \\ \\ \Rightarrow\frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}\ne\tan^{-1}(\frac{1}{2}) \end{gathered}[/tex][tex]\begin{gathered} \sin^{-1}(\frac{1}{2})=\frac{\pi}{6}\cong0.52 \\ \\ \frac{1}{\sin(\frac{1}{2})}\cong2.09 \\ \\ \Rightarrow\sin^{-1}(\frac{1}{2})\ne\frac{1}{\sin(\frac{1}{2})} \end{gathered}[/tex]Answer:
f. False
g. True
h. False
Notice that we can correct the statements f. and h. by using the correct notation:
[tex]\begin{gathered} \text{ f. }\frac{(\sin x)^{-1}}{(\cos x)^{-1}}=(\tan x)^{-1} \\ \\ \text{ h. }(\sin x)^{-1}=\frac{1}{\sin x} \end{gathered}[/tex]Number of Inches in a Mile An inch is approximately1.57828 x 10-5 mile. Find the reciprocal of this num-ber to determine the number of inches in a mile.
Answers
We are given that an inch is approximately 1.57828x10⁻⁵ mile.
[tex]1\: inch=1.57828\times10^{-5}\: \text{mile}[/tex]The reciprocal of this number will give us the number of inches in a mile.
[tex]\frac{1}{1.57828\times10^{-5}\: }=63360\: inches[/tex]Therefore, a mile is approximately 63360 inches.
[tex]1\: mile=63360\: \text{inches}[/tex]rewrite 2 5/8 into fraction
Answers
Answer:
i think 21/8
Step-by-step explanation:
because 2 times 8 plus 5 divided by 8 gives you 16 + 5 divided by 8 which is 21/8
Compare -2/3 to 3/4 is it equal, less.or greater
Answers
And
3/4 = 0.75
I suppose 3/4 is greater.
Answer:
less
Step-by-step explanation:
negative numbers are less than positive numbers
[tex]-\frac{2}{3} < \frac{3}{4}[/tex]
Hope this helps
INVERSES OF AN EXPONENTIAL FUNCTION 6). Fill in the chart. If needed, use a calculator and round to one decimal place.
Answers
We will have the following:
x f(x) = 4^x function(x,f(x)) inverse(f(x),x)
0 1 (0, 1) (1, 0)
1 4 (1, 4) (4, 0)
-1 1/4 (-1, 1/4) (1/4, -1)
2 16 (2, 16) (16, 2)
-2 1/16 (-2, 1/16) (1/16, -2)
Answer:
columns in order of 0/1/-1/2/-2
Step-by-step explanation:
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
Hi! I need some help with my precalculus homework question, please. Thank you for your time.
Answers
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
Explanation:The given point: (4, -1)
From the point: the coordinate tells us x = 4, y = -1
For a graph of function f, f(x) is the same as y
To represent the point (4, -1) as a funtion of x (that is f(x)), we will replace x in f(x) with the value of the x coordinate. The result when we replace it will the value of the y coordinate
when x = 4
f(4) = the value of the y coordinate
f(4) = -1
To complete the blanks:
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
describe the general trend of the unadjusted federal minimum wage from 1985 to 2020
Answers
From the graph we can infer that the general trend for the unadjusted federal minimum wage has been an increase.
Given a system of linear equations in three variables \Biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
You are going to solve the system by performing the following steps.
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate x from the two equations you got from part (1) and part (2).
(2pts) Find the solution for the given system.
(3pts) Check your solution for the given system.
Answers
Answer:
Step-by-step explanation:
n
if a || b, m<2=63°, and m<9=105°, find the missing measure of m<7=?
Answers
Vetical angles are on opposite sides of the intersection of two lines, in this case, when lines c and b intersect, <7 and <9 are formed, these angles are vertical and m<7 = m<9, then:
m<7 = 105°